Dependence of the maximal superconducting current on resonance frequency in shunted Josephson junction

We have investigated the phase dynamics and IV-characteristics of shunted Josephson junctions coupled to an $LC$ circuit. When the Josephson frequency $\omega_J$ is close to the eigen frequency $\omega_{rc}$ of the coupled resonance circuit, the IV-characteristic demonstrates an additional $rc$-branch. We have investigated the features of the $rc$-branch and of the superconducting current component for different values of the resonance frequency. It has been found that the maximal value of the superconducting current depends on the resonance frequency and that it increases when the end point of the $rc$-branch approaches the critical current. The dependence of the maximal superconducting current on the resonance frequency at different values of the dissipation parameter is peculiar, for the optimized maximum appears to be independent of the system parameters within $1\%$.